The Ramachandran plot is important to structural biology as it describes a peptide backbone in the context of its dominant degrees of freedom-the backbone dihedral angles φ and ψ (Ramachandran, Ramakrishnan & Sasisekharan, 1963). Since its introduction, the Ramachandran plot has been a crucial tool to characterize protein backbone features. However, the conformation or twist of a backbone as a function of φ and ψ has not been completely described for both cis and trans backbones. Additionally, little intuitive understanding is available about a peptide's conformation simply from knowing the φ and ψ values of a peptide (e.g., is the regular peptide defined by φ = ψ =  - 100°  left-handed or right-handed?). This report provides a new metric for backbone handedness (h) based on interpreting a peptide backbone as a helix with axial displacement d and angular displacement θ, both of which are derived from a peptide backbone's internal coordinates, especially dihedral angles φ, ψ and ω. In particular, h equals sin(θ)d∕|d|, with range [-1, 1] and negative (or positive) values indicating left(or right)-handedness. The metric h is used to characterize the handedness of every region of the Ramachandran plot for both cis (ω = 0°) and trans (ω = 180°) backbones, which provides the first exhaustive survey of twist handedness in Ramachandran (φ, ψ) space. These maps fill in the 'dead space' within the Ramachandran plot, which are regions that are not commonly accessed by structured proteins, but which may be accessible to intrinsically disordered proteins, short peptide fragments, and protein mimics such as peptoids. Finally, building on the work of (Zacharias & Knapp, 2013), this report presents a new plot based on d and θ that serves as a universal and intuitive alternative to the Ramachandran plot. The universality arises from the fact that the co-inhabitants of such a plot include every possible peptide backbone including cis and trans backbones. The intuitiveness arises from the fact that d and θ provide, at a glance, numerous aspects of the backbone including compactness, handedness, and planarity.

Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as α-helices and β-sheets. Secondary structure is characterized by the local rotational state of the protein backbone, quantified by two dihedral angles called ϕ and ψ. Particular types of secondary structure can generally be described by a single (diffuse) location on a two-dimensional plot drawn in the space of the angles ϕ and ψ, called a Ramachandran plot. By contrast, a recently-discovered nanomaterial made from peptoids, structural isomers of peptides, displays a secondary-structure motif corresponding to two regions on the Ramachandran plot [Mannige et al., Nature 526, 415 (2015)]. In order to describe such 'higher-order' secondary structure in a compact way we introduce here a means of describing regions on the Ramachandran plot in terms of a single Ramachandran number, [Formula: see text], which is a structurally meaningful combination of ϕ and ψ. We show that the potential applications of [Formula: see text] are numerous: it can be used to describe the geometric content of protein structures, and can be used to draw diagrams that reveal, at a glance, the frequency of occurrence of regular secondary structures and disordered regions in large protein datasets. We propose that [Formula: see text] might be used as an order parameter for protein geometry for a wide range of applications.

We report electron spin resonance measurements of donors in silicon at millikelvin temperatures using a superconducting LC planar micro-resonator and a Josephson parametric amplifier. The resonator includes a nanowire inductor, defining a femtoliter detection volume. Due to strain in the substrate, the donor resonance lines are heavily broadened. Single-spin to photon coupling strengths up to ∼ 3 kHz are observed. The single shot sensitivity is 120 ± 24 spins/Hahn echo, corresponding to ≈ 12 ± 3 spins / Hz for repeated acquisition.

Multiple organic functionalities can now be apportioned into nanoscale domains within a metal-coordinated framework, posing the following question: how do we control the resulting combination of "heterogeneity and order"? Here, we report the creation of a metal-organic framework, MOF-2000, whose two component types are incorporated in a 2:1 ratio, even when the ratio of component types in the starting solution is varied by an order of magnitude. Statistical mechanical modeling suggests that this robust 2:1 ratio has a nonequilibrium origin, resulting from kinetic trapping of component types during framework growth. Our simulations show how other "magic number" ratios of components can be obtained by modulating the topology of a framework and the noncovalent interactions between component types, a finding that may aid the rational design of functional multicomponent materials.

Electron spins are amongst the most coherent solid-state systems known. However, to be used in devices for quantum sensing and information processing applications, they must typically be placed near interfaces. Understanding and mitigating the impacts of such interfaces on the coherence and spectral properties of electron spins is critical to realizing such applications, but it is also challenging: Inferring such data from single-spin studies requires many measurements to obtain meaningful results, while ensemble measurements typically give averaged results that hide critical information. Here, we report a comprehensive study of the coherence of near-surface bismuth donor spins in 28-silicon at millikelvin temperatures. In particular, we use strain-induced frequency shifts caused by a metallic electrode to infer spatial maps of spin coherence as a function of position relative to the electrode. By measuring magnetic-field-insensitive clock transitions, we separate magnetic noise caused by surface spins from charge noise. Our results include quantitative models of the strain-split spin resonance spectra and extraction of paramagnetic impurity concentrations at the silicon surface. The interplay of these decoherence mechanisms for such near-surface electron spins is critical for their application in quantum technologies, while the combination of the strain splitting and clock transition extends the coherence lifetimes by up to 2 orders of magnitude, reaching up to 300 ms at a mean depth of only 100 nm. The technique we introduce here to spatially map coherence in near-surface ensembles is directly applicable to other spin systems of active interest, such as defects in diamond, silicon carbide, and rare earth ions in optical crystals.

We report long coherence times (up to 300 ms) for near-surface bismuth donor electron spins in silicon coupled to a superconducting microresonator, biased at a clock transition. This enables us to demonstrate the partial absorption of a train of weak microwave fields in the spin ensemble, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. Phase coherence and quantum statistics are preserved in the storage.